I am using SmoothingSplines.jl package to fit a spline curve to a time series. What I need is to test the fitted curve with a prior constant curve. (I need to know how like an how close two curves are) Is there any package to do such test? any help will be appreciated.

How do your time series and reference curve look like?

Spline curve can be in any shape, but constant curve is a straight line

The area dissimilarity between the two curves as defined here seems to be an interesting metric and it does not require a package to compute it.

do you mean - how close you fit a spline to a curve, or the closest point on a spline to a curve?

I want to know if the two curves are convergent

Do you just want the integral \Vert f - g \Vert^2 = \int |f(x)-g(x)|^2 dx of the difference? You could use QuadGK for that, I guess.

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